The covariety of numerical semigroups with fixed Frobenius number - Moreno-Frías, M. A.; Rosales, J. C. (Journal of algebraic combinatorics, 2024)
Denote by m ( S ) the multiplicity of a numerical semigroup S . A covariety is a nonempty family C of numerical semigroups that fulfils the following conditions: there is the minimum of C , the intersection of two elements of C is again an element of C and S \ { m ( S ) } ∈ C for all S ∈ C such that S ≠ min ( C ) . In this work we describe an algorithmic procedure to compute all the elements of C . We prove that there exists the smallest element of C containing a set of positive integers. We show that A ( F ) = { S ∣ S is a numerical semigroup with Frobenius number F } is a covariety, and we particularize the previous results in this covariety. Finally, we will see that there is the smallest covariety containing a finite set of numerical semigroups.